Of course photons carry information about whatever it interacted with. Photons don't have past (photons do not experience time). Photon's energy is the information as well as its polarization, direction from which it comes, etc.

Single photon is very small amount of information, you typically need more photons to get some kind of picture. But then when you think about it, the picture must have been carried by those photons so the information about the object IS in the photons you are receiving.

Now, photons coming away from black hole do not actually come from black hole. The photons that you can see are radiated by matter orbiting and falling into black hole. This carries no information from the black hole other than the geometry of the space (size/mass of the black hole), its angular velocity (angular momentum) and the charge which are the only measurable information about the black hole.